Implication Details
Claim: A category is accessible and is complete if and only if it is locally presentable.
Proof: This follows from one of equivalent formulations of locally presentable categories.
Show 41 categories using this implication
- trivial category
- category of abelian groups
- category of finitely generated abelian groups
- category of algebras
- category of Banach spaces with linear contractions
- category of commutative algebras
- category of commutative monoids
- category of commutative rings
- category of small categories
- simplex category
- category of fields
- category of countable groups
- category of Jónsson-Tarski algebras
- category of M-sets
- category of metric spaces with ∞ allowed
- category of monoids
- partially ordered collection of ordinal numbers
- category of partially ordered sets
- category of preordered sets
- category of finitely generated projective modules over the ring of dual numbers
- category of left modules over a ring
- category of left modules over a division ring
- category of left modules over a non-semisimple ring
- category of rings
- category of rngs
- category of semigroups
- category of sets
- category of set functions and commutative squares
- category of sets with finite-to-one maps
- category of non-empty sets
- category of pairs of sets
- category of sheaves
- category of abelian sheaves
- category of large vector spaces over a large field with a small basis
- preordered set of integers w.r.t. divisibility
- forked commutative square
- real interval [0,1]
- category of simplicial sets
- walking coreflexive pair
- walking isomorphism
- walking parallel pair